Survey on Classical Inequalities
Survey on Classical Inequalities provides a study of some of the well known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shann
- PDF / 29,145,320 Bytes
- 241 Pages / 453.54 x 680.31 pts Page_size
- 44 Downloads / 259 Views
Mathematics and Its Applications
Managing Editor: M. HAZEWINKEL Centre for Mathematics and Computer Science, Amsterdam, The Netherlands
Volume 517
Survey on Classical Inequalities by
Themistocles M. Rassias Department of Mathematics, National Technical University ofAthens, Zografou Campus, Athens, Greece
" ~.
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A c.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-94-010-5868-1 ISBN 978-94-011-4339-4 (eBook) DOI 10.1007/978-94-011-4339-4
Printed on acidjree paper
AII Rights Reserved © 2000 Springer Science+Business Media Dordrecht OriginaIly published by Kluwer Academic Publishers in 2000 No pact of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording Of by any information stofage and retrievaI system, without written permis sion from the copyright owner.
Contents
Preface .................................................
VII
Lyapunov Inequalities and their Applications Richard C. Brown and Don B. Hinton ............................ 1 Classical Hardy's and Carleman's Inequalities and Mixed Means Aleksandra CiimeSija and Josip Pecaric ......................... 27 Operator Inequalities Associated with Jensen's Inequality Frank Hansen ............................................. 67 Hardy-Littlewood-type Inequalities and their Factorized Enhancement LaszlO Leindler ............................................ 99 Shannon's and Related Inequalities in Information Theory M Mafic, C. E. M Pearce and J. Pecaric ....................... 127 Inequalities for Polynomial Zeros Gradimir V. Milovanovic and Themistocles M Rassias ............. 165 On Generalized Shannon Functional Inequality and its Applications Prasanna K Sahoo ........................................ 203 Weighted Lp-norm Inequalities in Convolutions Saburou Saitoh ........................................... 225 Index ................................................... 235 v
Preface
Survey on Classical Inequalities provides a study of some of the well known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, Shannon's and related inequalities, generalized Shannon functional inequality, operator inequalities associated with Jensen's inequality, weighted Lp-norm inequalities in convolutions, inequalities for polynomial zeros as well as applications in a number of problems of pure and applied mathematics. It is my pleasure to express my appreciation to the distinguished mathematicians who contributed to this volume. Finally, we wish to acknowledge the superb assistance provided by the staff of Kluwer Academic Publishers.
June 2000
Themistocles M. Rassias
Vll
LYAPUNOV INEQUALITIES AND THEIR APPLICATIONS RICHARD C. BROWN Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USA. email address:[email protected]
DO
